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DECODE- DISCRETE STRUCTURES AND THEORY OF LOGIC

H. R. Bhapkar ISBN-9789333217132
10% Discount
₹ 125.00
₹ 113.00
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UNIT-I
Set Theory : Introduction, Combination of sets, Multi sets, ordered pairs, Set Identities.
Relations : Definition, Operations on relations, Properties of relations, Composite Relations, Equality of relations, Order of relations.
Functions : Definition. Classification of functions, Operations on functions, Recursively defined functions.
Natural Numbers : Introduction, Mathematical Induction, Variants of Induction, Induction with Nonzero Base cases.
UNIT-II
Algebraic Structures : Definition, Groups, Subgroups and order, Cyclic Groups, Cosets, Lagrange's theorem, Normal Subgroups, Permutation and Symmetric groups, Group Homomorphism's, Definition and elementary properties of Rings and Fields, Integers modulo n.
UNIT-III
Partial order sets : Definition, Partial order sets, Combination of partial order sets, Hasse diagram.
Lattices : Definition, Properties of lattices - Bounded, Complemented, Modular and
Complete Lattice, Morphisms of lattices.
Boolean Algebra : Introduction, Axioms and Theorems of Boolean algebra, Algebraic manipulation of Boolean expressions. Simplification of Boolean Functions, Karnaugh maps, Logic gates, Digital circuits and Boolean algebra. Combinational and sequential Circuits.
UNIT-IV
Propositional Logic : Proposition, well formed formula, Truth tables, Tautology, Satisfiability, Contradiction, Algebra of proposition, Theory of Inference, Natural Deduction.
Predicate Logic : First order predicate, well formed formula of predicate, quantifiers, Inference theory of predicate logic.
UNIT-V
Trees : Definition, Binary tree, Binary tree traversal, Binary search tree.
Graphs : Definition and terminology, Representation of graphs, Multi graphs, Bipartite graphs, Planar graphs, Isomorphism and Homeomorphism of graphs, Euler and Hamiltonian paths, Graph coloring.
Recurrence Relation & Generating function : Recursive definition of functions, Recursive algorithms, Method of solving recurrences.
Combinatorics : Introduction, Counting Techniques, Pigeonhole Principle

 

UNIT-I
Set Theory : Introduction, Combination of sets, Multi sets, ordered pairs, Set Identities.
Relations : Definition, Operations on relations, Properties of relations, Composite Relations, Equality of relations, Order of relations.
Functions : Definition. Classification of functions, Operations on functions, Recursively defined functions.
Natural Numbers : Introduction, Mathematical Induction, Variants of Induction, Induction with Nonzero Base cases.
UNIT-II
Algebraic Structures : Definition, Groups, Subgroups and order, Cyclic Groups, Cosets, Lagrange's theorem, Normal Subgroups, Permutation and Symmetric groups, Group Homomorphism's, Definition and elementary properties of Rings and Fields, Integers modulo n.
UNIT-III
Partial order sets : Definition, Partial order sets, Combination of partial order sets, Hasse diagram.
Lattices : Definition, Properties of lattices - Bounded, Complemented, Modular and
Complete Lattice, Morphisms of lattices.
Boolean Algebra : Introduction, Axioms and Theorems of Boolean algebra, Algebraic manipulation of Boolean expressions. Simplification of Boolean Functions, Karnaugh maps, Logic gates, Digital circuits and Boolean algebra. Combinational and sequential Circuits.
UNIT-IV
Propositional Logic : Proposition, well formed formula, Truth tables, Tautology, Satisfiability, Contradiction, Algebra of proposition, Theory of Inference, Natural Deduction.
Predicate Logic : First order predicate, well formed formula of predicate, quantifiers, Inference theory of predicate logic.
UNIT-V
Trees : Definition, Binary tree, Binary tree traversal, Binary search tree.
Graphs : Definition and terminology, Representation of graphs, Multi graphs, Bipartite graphs, Planar graphs, Isomorphism and Homeomorphism of graphs, Euler and Hamiltonian paths, Graph coloring.
Recurrence Relation & Generating function : Recursive definition of functions, Recursive algorithms, Method of solving recurrences.
Combinatorics : Introduction, Counting Techniques, Pigeonhole Principle

 

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